Solve 2sqrt{144/81}+7^7*sqrt[3]{8}

$$2 \sqrt { \frac { 144 } { 81 } } + 7 ^ { 7 } \cdot \sqrt[ 3 ] { 8 }$$

Evaluate

$$\frac{4941266}{3}\approx 1647088.666666667$$

Solution Steps

Reduce the fraction \frac{144}{81} to lowest terms by extracting and canceling out 9.

$$2\sqrt{\frac{16}{9}}+7^{7}\sqrt[3]{8}$$

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$2\times \frac{4}{3}+7^{7}\sqrt[3]{8}$$

Multiply 2 and \frac{4}{3} to get \frac{8}{3}.

$$\frac{8}{3}+7^{7}\sqrt[3]{8}$$

Calculate 7 to the power of 7 and get 823543.

$$\frac{8}{3}+823543\sqrt[3]{8}$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{8}{3}+823543\times 2$$

Multiply 823543 and 2 to get 1647086.

$$\frac{8}{3}+1647086$$

Add \frac{8}{3} and 1647086 to get \frac{4941266}{3}.

$$\frac{4941266}{3}$$

Factor

$$\frac{2 \cdot 11 \cdot 224603}{3} = 1647088\frac{2}{3} = 1647088.6666666667$$